^{page 137 note 1} The bare references which are made here and there to friends and correspondents, who have assisted in the collection or verification of material, are wholly inadequate to express the measure of my indebtedness; and some kind offices may, I fear, have escaped even that meagre acknowledgement. Nevertheless I must content myself here with a brief gratiarum actio to those who have placed me under very special obligation, such as Mr. C. R. Peers, to whose encouragement the completion of the paper is mainly due; Mr. J. A. Herbert, who from the beginning spared no pains to note material which might be (and always was) of service, and gave me particular facilities for working at it; Mr. Max Rosenheim, whose knowledge of German seals, coins, and medals has been of great service; Dr. Kurt Regling, of Berlin, who has taken infinite pains in connexion especially with my inquiries about German seals, a subject on which I also owe much information to Dr. August Ritter von Loehr of the Vienna Museum; Prof. David Eugene Smith, of Columbia University, a recognized high authority on the archaeology of mathematics; Herr Lockner of Würzburg, to whom I owe some of the material from that neighbourhood; Mr. Mill Stephenson, who has noted examples from brasses; Dr. George Macdonald, of the Scotch Education Office, to whose inquiries are due some interesting examples from Scotland; Mr. H. B. Walters, who has placed his great knowledge of English bells at my disposal; and M. J. A. Blanchet, whose bibliographical notes on the subject have been very useful.

^{page 139 note 1} This applies especially to Mr. J. A. Herbert, whom I have mentioned above; but my warm thanks are also due to Dr. G. F. Warner and Mr. J. P. Gilson. I hasten to add that for any blunders of statement or interpretation which may be found in this and in the other sections of this paper, I alone am responsible.

^{page 139 note 2} 1136: de Terreros y Pando, E., Paleografia Española (1758), p. 102, pl. 12Google Scholar (530 of the Arab era). This is the date of the composition of the original work; the MS., so far as one can judge from an indifferent facsimile, appears to be of the thirteenth or fourteenth century. 1217: Terreros y Pando, p. 97, pl. 2. The script is certainly later. 1245: MS. Bibl. Strozzi, mentioned in nearly all the old treatises on the subject without verification, but doubted by modern authorities.

^{page 139 note 3} Tassin, and Toustain, , Nouveau Traité, iv, p. viiGoogle Scholar, describe a fine MS. of the eleventh century, containing the works of the Benedictine Guido d'Arezzo, who gives the numerals in a treatise on the art of reckoning. I have not succeeded in verifying this.

^{page 140 note 1} Mr. George Macdonald, of the Scotch Education Office, calls my attention to a form of 4 resembling + used in certain Scotch accounts, e.g. those of the Lord High Treasurer in the Register House, Edinburgh, where the 4 in 1545 is so made, or Andrew Halyburton's Ledgers (1493–1503).

^{page 141 note 1} A Heidelberg MS. from Kloster Salem shows the rivalry between the old and the new form in the years 1494–1499, the scribe using one form, the miniator another. Anzeiger für Kunde d. Deutschen Vorzeit, 1867, p. 161.

^{page 141 note 2} Found, e.g., on coins of Justinian I, struck in A. D. 541–2 (Wroth, W., Brit. Mus. Catal. of Imperial Byzantine Coins, i, p. 31, no. 56Google Scholar).

^{page 142 note 1} The Helmdon mantelpiece, a stock subject for discussion in the eighteenth century (Philosophical Transactions, 1731, i, fig. 55, at p. 190Google Scholar), supposed by many to bear the date 1133, cannot from its style have been earlier than the late fifteenth century. There was a somewhat similar oak chimney-piece at Widgel Hall, Herts., perhaps of 1516 (op. cit. 1735, p. 119), though the 16 has been explained as 1. G. The most ludicrous things have been written about a cruciform arrangement of figures at Castle Acre Priory (J. H. Bloom, Castle and Priory at Castle Acre, p. 25), which might conceivably be meant for 1480, but is certainly not so early. The figures 1393 on a brick illustrated by Mr. Haggard, Rider in A Farmer's Year (1906), p. 323Google Scholar, and since presented by him to the British Museum, appear from their style to date from the seventeenth century at the earliest. The iron scutcheon plate on the south door of the nave at Rendcombe Church, Gloucestershire, has six signs, of which the first, second, fourth, fifth, and sixth might be read as 10 417; but the third can hardly be explained as a figure. See Arch.Journ. vi. 291Google Scholar. A curious puzzle is presented by the date 1410 which was published in the Antiquary, xxxviii, p. 258Google Scholar, as from the brass of John de Campden in St. Cross, Winchester. No such date is to be seen on that brass, and all inquiry has failed to elicit an explanation. Either the facsimile given is a clever invention, for the forms are most plausible, or the person who sent it to the Antiquary has confused his notes as to the provenance of the date. It ought to be inquired into, as, if genuine, it (with the Fountains seal, Table L. 6) is the earliest English instance of the kind, saving the Wells numerals.

1485 occurs on a brass (of John Pulter) in a slab on an altar-tomb (of earlier date) in the north chapel of Hitchin parish church. The forms (modern 4 and 5) show that the numerals are later than the alleged date [Rubbing communicated by Mr. Murray Kendall]. The date 1489 given by Haines from a brass at Fressingfield, Suffolk, as being in Arabic numerals, is in Roman. 1490 on the brass of Wm. Fordmell, Vicar of Borden (Belcher, Kentish Brasses, i, p. 12Google Scholar), cannot be contemporary.

1265 on a bell at North Wootton near Wells (W. E. A. Axon, Proc. Manchester Lit. and Phil. Soc. 1876, pp. 173 ff.) is for 1625, as, Mr. H. B.Walters assures me, is proved by the work. The date 1489 on the bell at Eglingham, near Alnwick, also mentioned by Mr. Axon, is in Roman numerals. The signs which have been read 1508 on a bell at Rayleigh, Essex (Deedes and Walters, Church Bells of Essex, p. 40), are probably not numerals at all; the third sign looks like u or n. The reading I h u s (for Jesus) has been suggested, but is unlikely. I h n s for Johannes seems to have even less in its favour.

English dates which I have not found time or opportunity to verify or use, but which should be included in any corpus, are 1483 and 1494 from Fountains, 1489 and 1494 from Ripon, all with the old forms of 4 (Notes and Queries, ser. iv, p. 375). Mr. H. B. Walters informs me that early dates (for bells) occur on bells at Greystoke, Cumberland (1524), Wood Ditton, Cambridge (1544), and Elmley Castle, Worcs. (1559, now recast). Mr. G. L. M. Clauson has kindly procured for me rubbings of the dates on brasses in Eton College Chapel, viz. 1525, 1532 (Thomas Smith), 1545 (T. Edgcumb), and 1560 (Robert Stokins). The last shows the o with a slanting stroke through it.

^{page 143 note 1} Hereafter usually referred to simply as Anzeiger.

^{page 143 note 2} Some information may also be gained from Denzinger's articles in the Archiv des histor. Vereins von Unterfranken und Aschaffenburg, ix (1847), pp. 163. 178Google Scholar.

^{page 143 note 3} M.C.C. xi (1866), p. xlviiGoogle Scholar; Anzeiger (1876), p. 34.

^{page 144 note 1} A list of dated seals from 1369 onwards is given by Mauch in Anzeiger (1860), pp. 13 ff. See also E. Melly, Beiträge zur Sigillographie, and the various volumes of the M.C.C. referred to in the descriptions of Tables XXII-XXVI. Outside Germany early seals with Arabic numerals are very scarce, if indeed they occur at all before the sixteenth century. England, curiously enough, offers an isolated example as early as 1410 (Table L. 6). G. Demay, Inventaire des Sceaux de la Normandie (1881), p. vii, gives 1503 (Philippe de Clèves, Seigneur de Ravenstein), 1511 (Denis, Abbé de Loos), and 1515 (George, Duke of Saxony) apparently as the earliest instances of the use of Arabic numerals for this purpose known to him! For some information as to German seals (which, however, reached me too late for incorporation) I have to thank Dr. E. Gritzner of Weimar; he notes, for instance, the seals of the city of Munich of 1478, and of Weissenhorn in Bavaria (“S' civium in Wessenhoren 1476”). Dr. Theodor Hampe has kindly enabled me to obtain reproductions of a certain number of seals in the Germanisches Nationalmuseum at Nürnberg.

^{page 145 note 1} My thanks are due to Mr. Pollard and Mr. Scholderer for information with regard to early printed books, both German and Italian. I am assured that the mark of Caxton, which appears to combine an ancient 4 with a modern 7, should not be regarded as embodying a date.

^{page 146 note 1} The earliest occurrence of a date in Arabic numerals on a coin is found in the reign of Roger of Sicily, 533 A.H. = 1138 A.D. See Zambaur, E. v., Contributions à la Numism. Orientale, Num. Zeitschr., xxxvi, p. 83Google Scholar. But this occurs as part of an Arabic inscription. I owe the reference to Mrof. Allan.

^{page 147 note 1} The date 1391, on a painting by Spinello Aretino, will be found in the Supplementary Table L. 5, having been recently sent me by Mr. A. H. S. Yeames. 1464 is to be seen on a painting by Antonazzo Romano at Rieti (Rassegna d'Arte, 1909, p. 43) and on the banner with Our Lady protecting Perugia painted by Benedetto Bonfigli (Heywood, Perugia, at p. 299).

^{page 147 note 2} I have not included the two examples of 1519 on two pieces of Gubbio ware (Fortnum, p. 29) because of their suspiciously modern appearance.

^{page 147 note 3} See especially Guiffrey in Rev. Num. (1891), pp. 17–25, and Schlosser, J. von in Jahrb. d. kunsthist. Samml. des A. H. Kaiserhauses, xviii (1897), pp. 64 ff.Google Scholar

^{page 147 note 4} This table of Italian medals may claim to be fairly representative; but I have not been able to verify the following: 1455, Franc. Sforza (Armand, , Médailleurs italiens, ii. 26. 1Google Scholar, perhaps not contemporary); 1460, Borso d'Este (Heraeus, pl. lii. 1); 1467, plaquette by Enzola (Armand, i. 46. 13); 1490, Unknown woman (Armand, iii. 183D); 1498, Gioacchino della Torre (Armand, ii. 71. 10); 1498, Gianfrancesco della Rovere (Armand, ii. 106.22); not to mention some later than 1500. The dates 1488 on a medal of Francesco Accolti and 1498 on one of Ser Ceccone de' Baroni, and indeed the medals themselves, are false. (See Rev. Num. (1895), p. 460, and Burlington Magazine, Oct. 1909, p. 31.) The 8s in the date on the Accolti medal are like a recumbent ∞, a shape which comes in towards the end of the sixteenth century. See Table XII. 13.

^{page 147 note 5} Burger, F., Gesch. des florent. Grabmals (Strassburg, 1904), p. 34.Google Scholar Mr. A. H. S. Yeames has kindly reported to me a number of interesting examples; those of which I have been able to obtain clear photographs are entered in the Supplementary Tables. The others are from the armorial tablet in the Court of the Bargello at Florence: 1437, 1439, 1445, 1448, 1456, 1463, 1475, 1487. Other instances which I have noted, but not yet succeeded in verifying satisfactorily (even to the extent of learning whether they are in Arabic numerals at all), are: 1456, bust at Berlin, inscribed ALEXO DI LVCA MINI (Venturi, , Storia dell' arte ital, vi, p. 636Google Scholar, doubts the inscription); 1461, Berlin, terracotta copy of a Madonna by Bellano (Venturi, p. 487, suspects this inscription); 1475, tomb of Lorenzo Roverella, in church of San Giorgio di Ferrara, by Ambrogio da Milano (ib. p. 620); Cremona, Duomo, fragment of tomb of S. Arialdo, signed zo. ANTONIO. AMADEO. F. OPVS. 1484 (ib. p. 901).

^{page 147 note 6} L'Arte, ii (1899), p. 348Google Scholar.

^{page 148 note 1} I am obliged to Ritter A. von Loehr for the photograph from which the illustration is made.

^{page 148 note 2} See, for instance, von Schlosser, J., Werke der Kleinplastik in der Skulpturensammlung des A. H. Kaiserhauses, i, p. 4, pl. xGoogle Scholar.

^{page 148 note 3} Jahrbuch der kunsthist. Sammlungen des A. H Kaiserhauses, xxviii (1910), pp. 268, 271.Google Scholar

^{page 148 note 4} Müntz, E., Les Arts à la Cour des Papes, ii. pp. 27, 92 ffGoogle Scholar.

^{page 149 note 1} See Friedlein, G., Die Zahlzeichen und das elementare Rechnen der Griechen und Römer, Erlangen (1869), p. 12Google Scholar and pl. i. For other artificial systems see Wattenbach, Anleitung zu lat. Paläogr.⁴, p. 103.

^{page 177 note 1} See also Table XLIX.

^{page 183 note 1} See also Supplementary Table L. 11.

^{page 185 note 1} For a painting dated 1391, see Supplementary Table L. 5; for others of 1464, above, p. 147, note 1.

^{page 187 note 1} See also Supplementary Tables L, LI.